367 lines
12 KiB
FortranFixed
367 lines
12 KiB
FortranFixed
|
SUBROUTINE CTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
|
||
|
|
* .. Scalar Arguments ..
|
||
|
|
INTEGER INCX,K,LDA,N
|
||
|
|
CHARACTER DIAG,TRANS,UPLO
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
COMPLEX A(LDA,*),X(*)
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
* Purpose
|
||
|
|
* =======
|
||
|
|
*
|
||
|
|
* CTBMV performs one of the matrix-vector operations
|
||
|
|
*
|
||
|
|
* x := A*x, or x := A'*x, or x := conjg( A' )*x,
|
||
|
|
*
|
||
|
|
* where x is an n element vector and A is an n by n unit, or non-unit,
|
||
|
|
* upper or lower triangular band matrix, with ( k + 1 ) diagonals.
|
||
|
|
*
|
||
|
|
* Arguments
|
||
|
|
* ==========
|
||
|
|
*
|
||
|
|
* UPLO - CHARACTER*1.
|
||
|
|
* On entry, UPLO specifies whether the matrix is an upper or
|
||
|
|
* lower triangular matrix as follows:
|
||
|
|
*
|
||
|
|
* UPLO = 'U' or 'u' A is an upper triangular matrix.
|
||
|
|
*
|
||
|
|
* UPLO = 'L' or 'l' A is a lower triangular matrix.
|
||
|
|
*
|
||
|
|
* Unchanged on exit.
|
||
|
|
*
|
||
|
|
* TRANS - CHARACTER*1.
|
||
|
|
* On entry, TRANS specifies the operation to be performed as
|
||
|
|
* follows:
|
||
|
|
*
|
||
|
|
* TRANS = 'N' or 'n' x := A*x.
|
||
|
|
*
|
||
|
|
* TRANS = 'T' or 't' x := A'*x.
|
||
|
|
*
|
||
|
|
* TRANS = 'C' or 'c' x := conjg( A' )*x.
|
||
|
|
*
|
||
|
|
* Unchanged on exit.
|
||
|
|
*
|
||
|
|
* DIAG - CHARACTER*1.
|
||
|
|
* On entry, DIAG specifies whether or not A is unit
|
||
|
|
* triangular as follows:
|
||
|
|
*
|
||
|
|
* DIAG = 'U' or 'u' A is assumed to be unit triangular.
|
||
|
|
*
|
||
|
|
* DIAG = 'N' or 'n' A is not assumed to be unit
|
||
|
|
* triangular.
|
||
|
|
*
|
||
|
|
* Unchanged on exit.
|
||
|
|
*
|
||
|
|
* N - INTEGER.
|
||
|
|
* On entry, N specifies the order of the matrix A.
|
||
|
|
* N must be at least zero.
|
||
|
|
* Unchanged on exit.
|
||
|
|
*
|
||
|
|
* K - INTEGER.
|
||
|
|
* On entry with UPLO = 'U' or 'u', K specifies the number of
|
||
|
|
* super-diagonals of the matrix A.
|
||
|
|
* On entry with UPLO = 'L' or 'l', K specifies the number of
|
||
|
|
* sub-diagonals of the matrix A.
|
||
|
|
* K must satisfy 0 .le. K.
|
||
|
|
* Unchanged on exit.
|
||
|
|
*
|
||
|
|
* A - COMPLEX array of DIMENSION ( LDA, n ).
|
||
|
|
* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
|
||
|
|
* by n part of the array A must contain the upper triangular
|
||
|
|
* band part of the matrix of coefficients, supplied column by
|
||
|
|
* column, with the leading diagonal of the matrix in row
|
||
|
|
* ( k + 1 ) of the array, the first super-diagonal starting at
|
||
|
|
* position 2 in row k, and so on. The top left k by k triangle
|
||
|
|
* of the array A is not referenced.
|
||
|
|
* The following program segment will transfer an upper
|
||
|
|
* triangular band matrix from conventional full matrix storage
|
||
|
|
* to band storage:
|
||
|
|
*
|
||
|
|
* DO 20, J = 1, N
|
||
|
|
* M = K + 1 - J
|
||
|
|
* DO 10, I = MAX( 1, J - K ), J
|
||
|
|
* A( M + I, J ) = matrix( I, J )
|
||
|
|
* 10 CONTINUE
|
||
|
|
* 20 CONTINUE
|
||
|
|
*
|
||
|
|
* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
|
||
|
|
* by n part of the array A must contain the lower triangular
|
||
|
|
* band part of the matrix of coefficients, supplied column by
|
||
|
|
* column, with the leading diagonal of the matrix in row 1 of
|
||
|
|
* the array, the first sub-diagonal starting at position 1 in
|
||
|
|
* row 2, and so on. The bottom right k by k triangle of the
|
||
|
|
* array A is not referenced.
|
||
|
|
* The following program segment will transfer a lower
|
||
|
|
* triangular band matrix from conventional full matrix storage
|
||
|
|
* to band storage:
|
||
|
|
*
|
||
|
|
* DO 20, J = 1, N
|
||
|
|
* M = 1 - J
|
||
|
|
* DO 10, I = J, MIN( N, J + K )
|
||
|
|
* A( M + I, J ) = matrix( I, J )
|
||
|
|
* 10 CONTINUE
|
||
|
|
* 20 CONTINUE
|
||
|
|
*
|
||
|
|
* Note that when DIAG = 'U' or 'u' the elements of the array A
|
||
|
|
* corresponding to the diagonal elements of the matrix are not
|
||
|
|
* referenced, but are assumed to be unity.
|
||
|
|
* Unchanged on exit.
|
||
|
|
*
|
||
|
|
* LDA - INTEGER.
|
||
|
|
* On entry, LDA specifies the first dimension of A as declared
|
||
|
|
* in the calling (sub) program. LDA must be at least
|
||
|
|
* ( k + 1 ).
|
||
|
|
* Unchanged on exit.
|
||
|
|
*
|
||
|
|
* X - COMPLEX array of dimension at least
|
||
|
|
* ( 1 + ( n - 1 )*abs( INCX ) ).
|
||
|
|
* Before entry, the incremented array X must contain the n
|
||
|
|
* element vector x. On exit, X is overwritten with the
|
||
|
|
* tranformed vector x.
|
||
|
|
*
|
||
|
|
* INCX - INTEGER.
|
||
|
|
* On entry, INCX specifies the increment for the elements of
|
||
|
|
* X. INCX must not be zero.
|
||
|
|
* Unchanged on exit.
|
||
|
|
*
|
||
|
|
* Further Details
|
||
|
|
* ===============
|
||
|
|
*
|
||
|
|
* Level 2 Blas routine.
|
||
|
|
*
|
||
|
|
* -- Written on 22-October-1986.
|
||
|
|
* Jack Dongarra, Argonne National Lab.
|
||
|
|
* Jeremy Du Croz, Nag Central Office.
|
||
|
|
* Sven Hammarling, Nag Central Office.
|
||
|
|
* Richard Hanson, Sandia National Labs.
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
*
|
||
|
|
* .. Parameters ..
|
||
|
|
COMPLEX ZERO
|
||
|
|
PARAMETER (ZERO= (0.0E+0,0.0E+0))
|
||
|
|
* ..
|
||
|
|
* .. Local Scalars ..
|
||
|
|
COMPLEX TEMP
|
||
|
|
INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
|
||
|
|
LOGICAL NOCONJ,NOUNIT
|
||
|
|
* ..
|
||
|
|
* .. External Functions ..
|
||
|
|
LOGICAL LSAME
|
||
|
|
EXTERNAL LSAME
|
||
|
|
* ..
|
||
|
|
* .. External Subroutines ..
|
||
|
|
EXTERNAL XERBLA
|
||
|
|
* ..
|
||
|
|
* .. Intrinsic Functions ..
|
||
|
|
INTRINSIC CONJG,MAX,MIN
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
* Test the input parameters.
|
||
|
|
*
|
||
|
|
INFO = 0
|
||
|
|
IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
|
||
|
|
INFO = 1
|
||
|
|
ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
|
||
|
|
+ .NOT.LSAME(TRANS,'C')) THEN
|
||
|
|
INFO = 2
|
||
|
|
ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
|
||
|
|
INFO = 3
|
||
|
|
ELSE IF (N.LT.0) THEN
|
||
|
|
INFO = 4
|
||
|
|
ELSE IF (K.LT.0) THEN
|
||
|
|
INFO = 5
|
||
|
|
ELSE IF (LDA.LT. (K+1)) THEN
|
||
|
|
INFO = 7
|
||
|
|
ELSE IF (INCX.EQ.0) THEN
|
||
|
|
INFO = 9
|
||
|
|
END IF
|
||
|
|
IF (INFO.NE.0) THEN
|
||
|
|
CALL XERBLA('CTBMV ',INFO)
|
||
|
|
RETURN
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Quick return if possible.
|
||
|
|
*
|
||
|
|
IF (N.EQ.0) RETURN
|
||
|
|
*
|
||
|
|
NOCONJ = LSAME(TRANS,'T')
|
||
|
|
NOUNIT = LSAME(DIAG,'N')
|
||
|
|
*
|
||
|
|
* Set up the start point in X if the increment is not unity. This
|
||
|
|
* will be ( N - 1 )*INCX too small for descending loops.
|
||
|
|
*
|
||
|
|
IF (INCX.LE.0) THEN
|
||
|
|
KX = 1 - (N-1)*INCX
|
||
|
|
ELSE IF (INCX.NE.1) THEN
|
||
|
|
KX = 1
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Start the operations. In this version the elements of A are
|
||
|
|
* accessed sequentially with one pass through A.
|
||
|
|
*
|
||
|
|
IF (LSAME(TRANS,'N')) THEN
|
||
|
|
*
|
||
|
|
* Form x := A*x.
|
||
|
|
*
|
||
|
|
IF (LSAME(UPLO,'U')) THEN
|
||
|
|
KPLUS1 = K + 1
|
||
|
|
IF (INCX.EQ.1) THEN
|
||
|
|
DO 20 J = 1,N
|
||
|
|
IF (X(J).NE.ZERO) THEN
|
||
|
|
TEMP = X(J)
|
||
|
|
L = KPLUS1 - J
|
||
|
|
DO 10 I = MAX(1,J-K),J - 1
|
||
|
|
X(I) = X(I) + TEMP*A(L+I,J)
|
||
|
|
10 CONTINUE
|
||
|
|
IF (NOUNIT) X(J) = X(J)*A(KPLUS1,J)
|
||
|
|
END IF
|
||
|
|
20 CONTINUE
|
||
|
|
ELSE
|
||
|
|
JX = KX
|
||
|
|
DO 40 J = 1,N
|
||
|
|
IF (X(JX).NE.ZERO) THEN
|
||
|
|
TEMP = X(JX)
|
||
|
|
IX = KX
|
||
|
|
L = KPLUS1 - J
|
||
|
|
DO 30 I = MAX(1,J-K),J - 1
|
||
|
|
X(IX) = X(IX) + TEMP*A(L+I,J)
|
||
|
|
IX = IX + INCX
|
||
|
|
30 CONTINUE
|
||
|
|
IF (NOUNIT) X(JX) = X(JX)*A(KPLUS1,J)
|
||
|
|
END IF
|
||
|
|
JX = JX + INCX
|
||
|
|
IF (J.GT.K) KX = KX + INCX
|
||
|
|
40 CONTINUE
|
||
|
|
END IF
|
||
|
|
ELSE
|
||
|
|
IF (INCX.EQ.1) THEN
|
||
|
|
DO 60 J = N,1,-1
|
||
|
|
IF (X(J).NE.ZERO) THEN
|
||
|
|
TEMP = X(J)
|
||
|
|
L = 1 - J
|
||
|
|
DO 50 I = MIN(N,J+K),J + 1,-1
|
||
|
|
X(I) = X(I) + TEMP*A(L+I,J)
|
||
|
|
50 CONTINUE
|
||
|
|
IF (NOUNIT) X(J) = X(J)*A(1,J)
|
||
|
|
END IF
|
||
|
|
60 CONTINUE
|
||
|
|
ELSE
|
||
|
|
KX = KX + (N-1)*INCX
|
||
|
|
JX = KX
|
||
|
|
DO 80 J = N,1,-1
|
||
|
|
IF (X(JX).NE.ZERO) THEN
|
||
|
|
TEMP = X(JX)
|
||
|
|
IX = KX
|
||
|
|
L = 1 - J
|
||
|
|
DO 70 I = MIN(N,J+K),J + 1,-1
|
||
|
|
X(IX) = X(IX) + TEMP*A(L+I,J)
|
||
|
|
IX = IX - INCX
|
||
|
|
70 CONTINUE
|
||
|
|
IF (NOUNIT) X(JX) = X(JX)*A(1,J)
|
||
|
|
END IF
|
||
|
|
JX = JX - INCX
|
||
|
|
IF ((N-J).GE.K) KX = KX - INCX
|
||
|
|
80 CONTINUE
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Form x := A'*x or x := conjg( A' )*x.
|
||
|
|
*
|
||
|
|
IF (LSAME(UPLO,'U')) THEN
|
||
|
|
KPLUS1 = K + 1
|
||
|
|
IF (INCX.EQ.1) THEN
|
||
|
|
DO 110 J = N,1,-1
|
||
|
|
TEMP = X(J)
|
||
|
|
L = KPLUS1 - J
|
||
|
|
IF (NOCONJ) THEN
|
||
|
|
IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
|
||
|
|
DO 90 I = J - 1,MAX(1,J-K),-1
|
||
|
|
TEMP = TEMP + A(L+I,J)*X(I)
|
||
|
|
90 CONTINUE
|
||
|
|
ELSE
|
||
|
|
IF (NOUNIT) TEMP = TEMP*CONJG(A(KPLUS1,J))
|
||
|
|
DO 100 I = J - 1,MAX(1,J-K),-1
|
||
|
|
TEMP = TEMP + CONJG(A(L+I,J))*X(I)
|
||
|
|
100 CONTINUE
|
||
|
|
END IF
|
||
|
|
X(J) = TEMP
|
||
|
|
110 CONTINUE
|
||
|
|
ELSE
|
||
|
|
KX = KX + (N-1)*INCX
|
||
|
|
JX = KX
|
||
|
|
DO 140 J = N,1,-1
|
||
|
|
TEMP = X(JX)
|
||
|
|
KX = KX - INCX
|
||
|
|
IX = KX
|
||
|
|
L = KPLUS1 - J
|
||
|
|
IF (NOCONJ) THEN
|
||
|
|
IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
|
||
|
|
DO 120 I = J - 1,MAX(1,J-K),-1
|
||
|
|
TEMP = TEMP + A(L+I,J)*X(IX)
|
||
|
|
IX = IX - INCX
|
||
|
|
120 CONTINUE
|
||
|
|
ELSE
|
||
|
|
IF (NOUNIT) TEMP = TEMP*CONJG(A(KPLUS1,J))
|
||
|
|
DO 130 I = J - 1,MAX(1,J-K),-1
|
||
|
|
TEMP = TEMP + CONJG(A(L+I,J))*X(IX)
|
||
|
|
IX = IX - INCX
|
||
|
|
130 CONTINUE
|
||
|
|
END IF
|
||
|
|
X(JX) = TEMP
|
||
|
|
JX = JX - INCX
|
||
|
|
140 CONTINUE
|
||
|
|
END IF
|
||
|
|
ELSE
|
||
|
|
IF (INCX.EQ.1) THEN
|
||
|
|
DO 170 J = 1,N
|
||
|
|
TEMP = X(J)
|
||
|
|
L = 1 - J
|
||
|
|
IF (NOCONJ) THEN
|
||
|
|
IF (NOUNIT) TEMP = TEMP*A(1,J)
|
||
|
|
DO 150 I = J + 1,MIN(N,J+K)
|
||
|
|
TEMP = TEMP + A(L+I,J)*X(I)
|
||
|
|
150 CONTINUE
|
||
|
|
ELSE
|
||
|
|
IF (NOUNIT) TEMP = TEMP*CONJG(A(1,J))
|
||
|
|
DO 160 I = J + 1,MIN(N,J+K)
|
||
|
|
TEMP = TEMP + CONJG(A(L+I,J))*X(I)
|
||
|
|
160 CONTINUE
|
||
|
|
END IF
|
||
|
|
X(J) = TEMP
|
||
|
|
170 CONTINUE
|
||
|
|
ELSE
|
||
|
|
JX = KX
|
||
|
|
DO 200 J = 1,N
|
||
|
|
TEMP = X(JX)
|
||
|
|
KX = KX + INCX
|
||
|
|
IX = KX
|
||
|
|
L = 1 - J
|
||
|
|
IF (NOCONJ) THEN
|
||
|
|
IF (NOUNIT) TEMP = TEMP*A(1,J)
|
||
|
|
DO 180 I = J + 1,MIN(N,J+K)
|
||
|
|
TEMP = TEMP + A(L+I,J)*X(IX)
|
||
|
|
IX = IX + INCX
|
||
|
|
180 CONTINUE
|
||
|
|
ELSE
|
||
|
|
IF (NOUNIT) TEMP = TEMP*CONJG(A(1,J))
|
||
|
|
DO 190 I = J + 1,MIN(N,J+K)
|
||
|
|
TEMP = TEMP + CONJG(A(L+I,J))*X(IX)
|
||
|
|
IX = IX + INCX
|
||
|
|
190 CONTINUE
|
||
|
|
END IF
|
||
|
|
X(JX) = TEMP
|
||
|
|
JX = JX + INCX
|
||
|
|
200 CONTINUE
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of CTBMV .
|
||
|
|
*
|
||
|
|
END
|